DECISION THEORY

Decision theory is a body of knowledge and
related analytical techniques of different degrees of formality
designed to help a decision maker choose among a set of
alternatives in light of their possible consequences. Decision
theory can apply to conditions of certainty, risk, or
uncertainty. [decision UNDER certainty] means that each
alternative leads to one and only one consequence, and a choice
among alternatives is equivalent to a choice among consequences.
In [DECISION UNDER risk] each alternative will have one of
several possible consequences, and the probability of occurrence
for each consequence is known. Therefore, each alternative is
associated with a probability distribution, and a choice among
probability distributions. When the probability distributions
are unknown, one speaks about [DECISION UNDER uncertainty.]
Decision theory recognizes that the ranking produced by using a
criterion has to be consistent with the decision maker's
objectives and preferences. The theory offers a rich collection
of techniques and procedures to reveal preferences and to
introduce them into models of decision. It is not concerned with
defining objectives, designing the alternatives or assessing the
consequences; it usually considers them as given from outside, or
previously determined. Given a set of alternatives, a set of
consequences, and a correspondence between those sets, decision
theory offers conceptually simple procedures for choice. In a
decision situation under certainty the decision maker's
preferences are simulated by a single-attribute or
MULTIATTRIBUTE VALUE FUNCTION that introduces ordering on the
set of consequences and thus also ranks the alternatives.
Decision theory for risk conditions is based on the concept of
utility (see utility, sense 2). The decision maker's
preferences for the mutually exclusive consequences of an
alternative are described by a utilityfunction that permits
calculation of the EXPECTED UTILITY for each alternative. The
alternative with the highest expected utility is considered the
most preferable. For the case of uncertainty, decision theory
offers two main approaches. The first exploits criteria of
choice developed in a broader context by game theory, as for
example the [MAX-MIN RULE,] where we choose the alternative such
that the worst possible consequence of the chosen alternative is
better than (or equal to) the best possible consequence of any
other alternative. The second approach is to reduce the
uncertainty case to the case of risk by using SUBJECTIVE
PROBABILITIES, based on expert assessments or on analysis of
previous decisions made in similar circumstances. See also:
game theory, optimization, utility,value (IIASA)